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DTIC ADA121470: Testing Hypotheses Which Are Unions of Linear Subspaces.

by: Defense Technical Information Center

Publication date: 1982-09-01

Topics: DTIC Archive, Berger,Roger L, FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS, *LINEAR SYSTEMS, *HYPOTHESES, *ECOLOGY, *POPULATION(MATHEMATICS), RATIOS, COMPUTATIONS, STATISTICAL TESTS, MATRICES(MATHEMATICS), DISPLACEMENT,

Collection: dticarchive; additional_collections

Language: English

The likelihood ratio test (LRT) for hypotheses which are unions of linear subspaces is derived for the normal theory linear model. A more powerful variant of the LRT is proposed for the case in which the subspaces are not all of the same dimension. A theorem is proved which may be used to identify hypotheses which are unions of linear subspaces. Some hypotheses, of particular relevance in ecology, concerning the spacings between normal means are shown to be unions of linear subspaces and are therefore testable using the LRT. Finally, the computation of the LRT statistic is discussed. (Author)